Final answer:
The half-life of a reaction is determined by the order of the reaction. For a first-order reaction, it is found using the expression t1/2 = 0.693/k. For a second-order reaction, the half-life can be calculated with t1/2 = 1 / (k*[Initial Concentration]), and an example of a second-order half-life calculation is 18 minutes with given parameters.
Step-by-step explanation:
To calculate the half-life of a reaction, we use different equations contingent on the order of the reaction. For a first-order reaction, the half-life can be found by using the expression t1/2 = 0.693/k, where k represents the rate constant. This equation stems from the natural logarithm of 2, expressed as ln(2) ≈ 0.693, and is significant for processes like radioactive decay of 14C, where t1/2 is known to be 5730 years.
However, for a second-order reaction, such as one initiated with a 0.200 mol L-1 reactant solution exhibiting a rate constant of 0.0576 L mol-1 min-1, we utilize the second-order half-life equation t1/2 = 1 / (k*[Initial Concentration]), resulting in a half-life of 18 minutes for this specific case.
It is important to note for first-order reactions, after n half-lives, the amount of reactant left is (1/2)n times the initial concentration. For example, with n being 6.00 and the initial amount I being 1.00 gram of reactant, R = (1.00 gram)/(26.00).